1. Pre-AP Chemistry
Measurements
and
Calculations

2. Nature of Measurement Measurement - quantitative observation
consisting of 2 parts
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x Joule seconds

3. Why Is there Uncertainty?
Measurements are performed by people with instruments
No instrument can read to an infinite number of decimal places, & no person is perfect!
A measurment is only as reliable as the equipment that is used and the person making the measurement!

4. Uncertainty in Measurement
When making a measurement, the last digit MUST be estimated.
This is to make the measurement as precise and accurate as possible.
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

5. Reading Measurements

6. Reading Measurements

7. Reading Measurements

8. Reading Measurements

9. Reading Measurements

10. Reading Measurements

11. Sig Fig Practice #1 1.0070 m  5 sig figs 17.10 kg  4 sig figs
How many significant figures in each of the following?
m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 
2 sig figs

12. Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =
12.76  13 (2 sig figs)

13. Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
240 m/s
lb x 3.23 ft
lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
g/mL
2.96 g/mL

14. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.
 18.7 (3 sig figs)
Last place in least precise measurement

15. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL

16. The Fundamental SI Units (le Système International, SI)

17. SI Units

18. Derived SI Units we will use
Volume = length x length x length
SI unit = the Liter (L)
Density = mass / volume
SI unit = g / mL
Molar Mass = mass / mol
SI unit = g/mol
Concentration = mol / volume
SI unit = Molarity (M) = mol / L

19. SI Prefixes Common to Chemistry
Unit Abbr.
Kilo k
Centi c
Milli m
Micro 
Nano n

20. SI Unit Conversions How to convert between units
NOT JUST MOVING DECIMALS!
Must use a conversion factor for the prefix you are working with.
Conversion Factors:
1 kilo________ = 1000 ________
100 centi ________ = 1 ________
1000 milli ________ = 1 ________
1,000,000 micro ________ = 1 ________
1,000,000,000 nano ________ = 1 ________
Kilo
BASE UNIT
Centi
Milli
Micro
Nano
Kilometer
METER
Centimeter
Millimeter
Micrometer
Nanometer
Largest
Smallest

21. Using Conversion Factors
Ex: 1000 mill ________ = 1 ________
Given 4.5 g, determine the # of mg.
UNITS ARE IMPORTANT!!!!
4.5 g  ____ mg
1st Step- We will multiply and divide!
2nd- Units you know go on bottom, units you don’t go on top
3rd- Put the numbers in the equation that match the units from the conversion factor.
4th- Solve! g mg
4.5 g mg
1000 1
4500

22. Conversion Practice Convert: 220 m  km Convert : 22,000 us  s
Conversion factor: 1 km = 1000m
Convert : 22,000 us  s
Conversion factor: 1,000,000 us = 1 s 1
1000 m km
220 m km
.22 1
1,000,000 us s
22,000 us s
.022

23. 2 Step Conversions Convert: 8.4 mL  nL
No conversion factor between mL & nL
Do have conversion factors mL L & L  nL
Conversion factor: 1 L = 1000 mL
Conversion factor: 1,000,000,000 nL = 1 L 1
1000 mL L
8.4 mL L
.0084
1,000,000,000 1 L nL
.0084 L nL
8,400,000

24. Constructing Conversion Factors, i.e. Derived Units
Any equality between numbers with different units is a conversion factor!
EX: 1 week = 7 days, 1 day = 24 hrs, hr = 60 min, 1 min = 70 heart beats.
Derived Units combine different units together to measure 1 thing. EX
Density = mass / volume.
Volume = length x length x length

25. Constructing Conversion Factors, i.e. Derived Units
1 week = 7 days day = 24 hrs hr = 60 min min = 70 heart beats
Given the above info
What is the derived units for:
# of heart beats per minute?
Hours per week?
Calculate how many heartbeats would occur in 3.5 weeks.

26. Scientific Notation notes

27. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

28. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
???????????????????????????????????

29. Scientific Notation:
A method of representing very large or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is an integer

30. . 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

31. 2.5 x 109
The exponent is the number of places we moved the decimal.

32. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

33. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

34. Making Measurements- Error

35. Precision and Accuracy
Accuracy: How close a measurement is to the ACCEPTED VALUE.
Precision: How close measurements are to EACHOTHER.
Neither accurate nor precise
Precise but not accurate
Precise AND accurate

36. Precision and Accuracy
Is it better to be accurate or precise?
WHY?

37. Percent Error
Percent Error is a way of determining how “off” a measurement is from the accepted value.
Accepted Value – Experimental Value
Accepted Value
X 100
% Error =

38. What is it, Why is it important?
Density-
What is it, Why is it important?
Density is the amount of mass per unit volume an object contains.
D = m/v
This is a DERIVED UNIT
Density is important because it is an INTENSIVE PROPERTY
This means it doesn’t matter how much of a substance you have.
Ex: 1 ounce of gold and 1 ton of gold have the exact same density!

39. Graphical Relationships
Direct Proportions
The quotient of two variables is a constant
As the value of one variable increases, the other must also increase
As the value of one variable decreases, the other must also decrease
The graph of a direct proportion is a straight line

40. Graphical Relationships Inverse (or Indirect) Proportions
The product of two variables is a constant
As the value of one variable increases, the other must decrease
As the value of one variable decreases, the other must increase
The graph of an inverse proportion is a hyperbola

41. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
ADDITION AND SUBTRACTION

42. Review: M x 10n Scientific notation expresses a number in the form:
n is an integer
1  M  10

43. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106 7
x 106

44. The same holds true for subtraction in scientific notation.
4 x 106
- 3 x 106 1
x 106

45. If the exponents are NOT the same, we must move a decimal to make them the same.

46.  Is this good scientific notation?
Student A
 Is this good scientific notation?
x 105
4.00 x 106
x 105
NO!
43.00
x 105
To avoid this problem, move the decimal on the smaller number!
= x 106

47.  Is this good scientific notation?
4.00 x 106
Student B
x 105
.30 x 106
YES!
 Is this good scientific notation?
4.30
x 106

48. A Problem for you…
2.37 x 10-6
x 10-4

49. Solution…
x 10-6
2.37 x 10-6
x 10-4
x 10-4
x 10-4

50. Rules for Counting Significant Figures - Details
Nonzero integers always count as significant figures.
3456 has
4 sig figs.

51. Rules for Counting Significant Figures - Details
Zeros
- Leading zeros do not count as
significant figures.
has
3 sig figs.

52. Rules for Counting Significant Figures - Details
Zeros
- Captive zeros always count as
significant figures.
16.07 has
4 sig figs.

53. Rules for Counting Significant Figures - Details
Zeros
Trailing zeros are significant only if the number contains a decimal point.
9.300 has
4 sig figs.

54. Rules for Counting Significant Figures - Details
Exact numbers have an infinite number of significant figures.
1 inch = cm, exactly

55. Direct Proportions The quotient of two variables is a constant
As the value of one variable increases, the other must also increase
As the value of one variable decreases, the other must also decrease
The graph of a direct proportion is a straight line

56. Inverse Proportions The product of two variables is a constant
As the value of one variable increases, the other must decrease
As the value of one variable decreases, the other must increase
The graph of an inverse proportion is a hyperbola